Abstract

For the thin-film solar cells embedded with nanostructures at their rear dielectric layer, the shape and location of the nanostructures are crucial for higher conversion efficiency. A novel two-level hierarchical nanostructure (a sphere evenly covered with half truncated smaller spheres) can facilitate stronger intensity and wider scattering angles due to the coexistence of the merits of the nanospheres in two scales. We show in this article that the evolutionary algorithm allows for obtaining the optimal parameters of this two-scale nanostructure in terms of the maximization of the short circuit current density. In comparison with the thin-film solar cells with convex and flat metal back, whose parameters are optimized singly, the short circuit current density is improved by 7.48% and 10.23%, respectively. The exploration of such a two-level hierarchical nanostructure within an optimization framework signifies a new domain of study and allows to better identify the role of sophisticated shape in light trapping in the absorbing film, which is believed to be the main reason for the enhancement of short circuit current density.

© 2013 OSA

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2012

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

X. Huang, Y. M. Xie, B. Jia, Q. Li, S. W. Zhou, “Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity,” Struct. Multidisc. Optim. 46(3), 385–398 (2012).
[CrossRef]

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

M. d’Avezac, J. W. Luo, T. Chanier, A. Zunger, “Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors,” Phys. Rev. Lett. 108(2), 027401 (2012).
[CrossRef] [PubMed]

2011

M. Yang, Z. P. Fu, F. Lin, X. Zhu, “Incident angle dependence of absorption enhancement in plasmonic solar cells,” Opt. Express 19(S4Suppl 4), A763–A771 (2011).
[CrossRef] [PubMed]

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, Q. Li, “Topology optimization for negative permeability metamaterials using level-set algorithm,” Acta Mater. 59(7), 2624–2636 (2011).
[CrossRef]

2010

2009

R. Dewan, D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[CrossRef]

R. Dewan, M. Marinkovic, R. Noriega, S. Phadke, A. Salleo, D. Knipp, “Light trapping in thin-film silicon solar cells with submicron surface texture,” Opt. Express 17(25), 23058–23065 (2009).
[CrossRef] [PubMed]

F. J. Beck, A. Polman, K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[CrossRef]

2008

2007

S. Pillai, K. R. Catchpole, T. Trupke, M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101, 104309 (2007).
[CrossRef]

S. S. Lo, C. C. Chen, F. Garwe, T. Pertch, “Broad-band anti-reflection coupler for a:Si thin-film solar cell,” J. Phys. D Appl. Phys. 40(3), 754–758 (2007).
[CrossRef]

2003

L. F. Shen, Z. Ye, S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

2001

C. Eisele, C. E. Nebel, M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

2000

1999

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285(5428), 692–698 (1999).
[CrossRef] [PubMed]

B. Rech, H. Wagner, “Potential of amorphous silicon for solar cells,” Appl. Phys., A Mater. Sci. Process. 69(2), 155–167 (1999).
[CrossRef]

1997

R. Storn, K. Price, “Differential Evolution – A simple and efficient heuristic for global optimization over continuous spaces,” J. Glob. Optim. 11(4), 341–359 (1997).
[CrossRef]

1996

O. Sigmund, S. Torquato, “Composites with extremal thermal expansion coefficients,” Appl. Phys. Lett. 69(21), 3203–3205 (1996).
[CrossRef]

1994

E. A. Rakhmanov, E. B. Saff, Y. M. Zhou, “Minimal discrete energy on the sphere,” Math. Res. Lett. 1, 647–662 (1994).

1993

Y. M. Xie, G. P. Steven, “A simple evolutionary procedure for structural optimization,” Comput. Struc. 49(5), 885–896 (1993).
[CrossRef]

1986

P. Campbell, M. A. Green, “The limiting efficiency of silicon solar-cells under concentrated sunlight,” IEEE Trans. Electron. Dev. 33(2), 234–239 (1986).
[CrossRef]

1966

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Atwater, H. A.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

Beck, F. J.

F. J. Beck, A. Polman, K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[CrossRef]

Beuthan, J.

Cai, B. Y.

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

Campbell, P.

P. Campbell, M. A. Green, “The limiting efficiency of silicon solar-cells under concentrated sunlight,” IEEE Trans. Electron. Dev. 33(2), 234–239 (1986).
[CrossRef]

Catchpole, K. R.

F. J. Beck, A. Polman, K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[CrossRef]

K. R. Catchpole, A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Chanier, T.

M. d’Avezac, J. W. Luo, T. Chanier, A. Zunger, “Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors,” Phys. Rev. Lett. 108(2), 027401 (2012).
[CrossRef] [PubMed]

Chen, C. C.

S. S. Lo, C. C. Chen, F. Garwe, T. Pertch, “Broad-band anti-reflection coupler for a:Si thin-film solar cell,” J. Phys. D Appl. Phys. 40(3), 754–758 (2007).
[CrossRef]

Chen, C. H.

Chen, P. Y.

Chen, X.

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

Chen, Y. H.

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, Q. Li, “Topology optimization for negative permeability metamaterials using level-set algorithm,” Acta Mater. 59(7), 2624–2636 (2011).
[CrossRef]

d’Avezac, M.

M. d’Avezac, J. W. Luo, T. Chanier, A. Zunger, “Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors,” Phys. Rev. Lett. 108(2), 027401 (2012).
[CrossRef] [PubMed]

Derkacs, D.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101, 104309 (2007).
[CrossRef]

Dewan, R.

Eisele, C.

C. Eisele, C. E. Nebel, M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

Fahim, N.

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

Ferry, V. E.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

Fu, Z. P.

Garwe, F.

S. S. Lo, C. C. Chen, F. Garwe, T. Pertch, “Broad-band anti-reflection coupler for a:Si thin-film solar cell,” J. Phys. D Appl. Phys. 40(3), 754–758 (2007).
[CrossRef]

Green, M. A.

S. Pillai, K. R. Catchpole, T. Trupke, M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

P. Campbell, M. A. Green, “The limiting efficiency of silicon solar-cells under concentrated sunlight,” IEEE Trans. Electron. Dev. 33(2), 234–239 (1986).
[CrossRef]

Gu, M.

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

He, S. L.

L. F. Shen, Z. Ye, S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

Hielscher, A. H.

Huang, X.

X. Huang, Y. M. Xie, B. Jia, Q. Li, S. W. Zhou, “Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity,” Struct. Multidisc. Optim. 46(3), 385–398 (2012).
[CrossRef]

Jia, B.

X. Huang, Y. M. Xie, B. Jia, Q. Li, S. W. Zhou, “Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity,” Struct. Multidisc. Optim. 46(3), 385–398 (2012).
[CrossRef]

Jia, B. H.

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

Keppner, H.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285(5428), 692–698 (1999).
[CrossRef] [PubMed]

Klose, A. D.

Knipp, D.

Li, H. B. T.

Li, Q.

X. Huang, Y. M. Xie, B. Jia, Q. Li, S. W. Zhou, “Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity,” Struct. Multidisc. Optim. 46(3), 385–398 (2012).
[CrossRef]

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, Q. Li, “Topology optimization for negative permeability metamaterials using level-set algorithm,” Acta Mater. 59(7), 2624–2636 (2011).
[CrossRef]

S. W. Zhou, Q. Li, “Design of three-dimensional periodic metamaterials for electromagnetic properties,” IEEE Trans. Microw. Theory Tech. 58, 910–916 (2010).
[CrossRef]

Li, W.

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, Q. Li, “Topology optimization for negative permeability metamaterials using level-set algorithm,” Acta Mater. 59(7), 2624–2636 (2011).
[CrossRef]

Li, X. P.

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

Lim, S. H.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101, 104309 (2007).
[CrossRef]

Lin, F.

Lo, S. S.

S. S. Lo, C. C. Chen, F. Garwe, T. Pertch, “Broad-band anti-reflection coupler for a:Si thin-film solar cell,” J. Phys. D Appl. Phys. 40(3), 754–758 (2007).
[CrossRef]

Luo, J. W.

M. d’Avezac, J. W. Luo, T. Chanier, A. Zunger, “Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors,” Phys. Rev. Lett. 108(2), 027401 (2012).
[CrossRef] [PubMed]

Mar, W.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101, 104309 (2007).
[CrossRef]

Marinkovic, M.

Matheu, P.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101, 104309 (2007).
[CrossRef]

Nebel, C. E.

C. Eisele, C. E. Nebel, M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

Ni, W. X.

Nishikawa, T.

Noriega, R.

Ouyang, Z.

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

Pertch, T.

S. S. Lo, C. C. Chen, F. Garwe, T. Pertch, “Broad-band anti-reflection coupler for a:Si thin-film solar cell,” J. Phys. D Appl. Phys. 40(3), 754–758 (2007).
[CrossRef]

Phadke, S.

Pillai, S.

S. Pillai, K. R. Catchpole, T. Trupke, M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Polman, A.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

F. J. Beck, A. Polman, K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[CrossRef]

K. R. Catchpole, A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

Price, K.

R. Storn, K. Price, “Differential Evolution – A simple and efficient heuristic for global optimization over continuous spaces,” J. Glob. Optim. 11(4), 341–359 (1997).
[CrossRef]

Qiao, Q.

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

Rakhmanov, E. A.

E. A. Rakhmanov, E. B. Saff, Y. M. Zhou, “Minimal discrete energy on the sphere,” Math. Res. Lett. 1, 647–662 (1994).

Rech, B.

B. Rech, H. Wagner, “Potential of amorphous silicon for solar cells,” Appl. Phys., A Mater. Sci. Process. 69(2), 155–167 (1999).
[CrossRef]

Saff, E. B.

E. A. Rakhmanov, E. B. Saff, Y. M. Zhou, “Minimal discrete energy on the sphere,” Math. Res. Lett. 1, 647–662 (1994).

Saha, J. K.

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

Salleo, A.

Schropp, R. E. I.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

Shah, A.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285(5428), 692–698 (1999).
[CrossRef] [PubMed]

Shen, L. F.

L. F. Shen, Z. Ye, S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

Shi, Z. R.

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

Sigmund, O.

O. Sigmund, S. Torquato, “Composites with extremal thermal expansion coefficients,” Appl. Phys. Lett. 69(21), 3203–3205 (1996).
[CrossRef]

Spinelli, P.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

Steven, G. P.

Y. M. Xie, G. P. Steven, “A simple evolutionary procedure for structural optimization,” Comput. Struc. 49(5), 885–896 (1993).
[CrossRef]

Stokes, N.

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

Storn, R.

R. Storn, K. Price, “Differential Evolution – A simple and efficient heuristic for global optimization over continuous spaces,” J. Glob. Optim. 11(4), 341–359 (1997).
[CrossRef]

Stutzmann, M.

C. Eisele, C. E. Nebel, M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

Sun, G. Y.

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, Q. Li, “Topology optimization for negative permeability metamaterials using level-set algorithm,” Acta Mater. 59(7), 2624–2636 (2011).
[CrossRef]

Torquato, S.

O. Sigmund, S. Torquato, “Composites with extremal thermal expansion coefficients,” Appl. Phys. Lett. 69(21), 3203–3205 (1996).
[CrossRef]

Torres, P.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285(5428), 692–698 (1999).
[CrossRef] [PubMed]

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Tsai, J. H.

Tscharner, R.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285(5428), 692–698 (1999).
[CrossRef] [PubMed]

van de Groep, J.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

van Lare, M.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

Ventura, M. J.

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

Verhagen, E.

Verschuuren, M. A.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

Wagner, H.

B. Rech, H. Wagner, “Potential of amorphous silicon for solar cells,” Appl. Phys., A Mater. Sci. Process. 69(2), 155–167 (1999).
[CrossRef]

Walters, R. J.

Wang, H.

Wang, Y. Q.

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

Wyrsch, N.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285(5428), 692–698 (1999).
[CrossRef] [PubMed]

Xie, Y. M.

X. Huang, Y. M. Xie, B. Jia, Q. Li, S. W. Zhou, “Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity,” Struct. Multidisc. Optim. 46(3), 385–398 (2012).
[CrossRef]

Y. M. Xie, G. P. Steven, “A simple evolutionary procedure for structural optimization,” Comput. Struc. 49(5), 885–896 (1993).
[CrossRef]

Yamada, N.

Yang, M.

Ye, Z.

L. F. Shen, Z. Ye, S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Yu, E. T.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101, 104309 (2007).
[CrossRef]

Zhou, S. W.

X. Huang, Y. M. Xie, B. Jia, Q. Li, S. W. Zhou, “Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity,” Struct. Multidisc. Optim. 46(3), 385–398 (2012).
[CrossRef]

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, Q. Li, “Topology optimization for negative permeability metamaterials using level-set algorithm,” Acta Mater. 59(7), 2624–2636 (2011).
[CrossRef]

S. W. Zhou, Q. Li, “Design of three-dimensional periodic metamaterials for electromagnetic properties,” IEEE Trans. Microw. Theory Tech. 58, 910–916 (2010).
[CrossRef]

Zhou, Y. M.

E. A. Rakhmanov, E. B. Saff, Y. M. Zhou, “Minimal discrete energy on the sphere,” Math. Res. Lett. 1, 647–662 (1994).

Zhu, X.

Zunger, A.

M. d’Avezac, J. W. Luo, T. Chanier, A. Zunger, “Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors,” Phys. Rev. Lett. 108(2), 027401 (2012).
[CrossRef] [PubMed]

Acta Mater.

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, Q. Li, “Topology optimization for negative permeability metamaterials using level-set algorithm,” Acta Mater. 59(7), 2624–2636 (2011).
[CrossRef]

Appl. Phys. Lett.

O. Sigmund, S. Torquato, “Composites with extremal thermal expansion coefficients,” Appl. Phys. Lett. 69(21), 3203–3205 (1996).
[CrossRef]

K. R. Catchpole, A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

Appl. Phys., A Mater. Sci. Process.

B. Rech, H. Wagner, “Potential of amorphous silicon for solar cells,” Appl. Phys., A Mater. Sci. Process. 69(2), 155–167 (1999).
[CrossRef]

Comput. Struc.

Y. M. Xie, G. P. Steven, “A simple evolutionary procedure for structural optimization,” Comput. Struc. 49(5), 885–896 (1993).
[CrossRef]

IEEE Trans. Antenn. Propag.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

IEEE Trans. Electron. Dev.

P. Campbell, M. A. Green, “The limiting efficiency of silicon solar-cells under concentrated sunlight,” IEEE Trans. Electron. Dev. 33(2), 234–239 (1986).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

S. W. Zhou, Q. Li, “Design of three-dimensional periodic metamaterials for electromagnetic properties,” IEEE Trans. Microw. Theory Tech. 58, 910–916 (2010).
[CrossRef]

J. Appl. Phys.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101, 104309 (2007).
[CrossRef]

F. J. Beck, A. Polman, K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[CrossRef]

C. Eisele, C. E. Nebel, M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

R. Dewan, D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[CrossRef]

J. Glob. Optim.

R. Storn, K. Price, “Differential Evolution – A simple and efficient heuristic for global optimization over continuous spaces,” J. Glob. Optim. 11(4), 341–359 (1997).
[CrossRef]

J. Opt.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012).
[CrossRef]

J. Phys. D Appl. Phys.

S. S. Lo, C. C. Chen, F. Garwe, T. Pertch, “Broad-band anti-reflection coupler for a:Si thin-film solar cell,” J. Phys. D Appl. Phys. 40(3), 754–758 (2007).
[CrossRef]

Math. Res. Lett.

E. A. Rakhmanov, E. B. Saff, Y. M. Zhou, “Minimal discrete energy on the sphere,” Math. Res. Lett. 1, 647–662 (1994).

Nano Lett.

X. Chen, B. H. Jia, J. K. Saha, B. Y. Cai, N. Stokes, Q. Qiao, Y. Q. Wang, Z. R. Shi, M. Gu, “Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles,” Nano Lett. 12(5), 2187–2192 (2012).
[CrossRef] [PubMed]

Nanophotonics

M. Gu, Z. Ouyang, B. H. Jia, N. Stokes, X. Chen, N. Fahim, X. P. Li, M. J. Ventura, Z. R. Shi, “Nanoplasmonics: a frontier of photovoltaic solar cells,” Nanophotonics 1(3-4), 235–248 (2012).
[CrossRef]

Nat. Mater.

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

L. F. Shen, Z. Ye, S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

Phys. Rev. Lett.

M. d’Avezac, J. W. Luo, T. Chanier, A. Zunger, “Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors,” Phys. Rev. Lett. 108(2), 027401 (2012).
[CrossRef] [PubMed]

Science

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285(5428), 692–698 (1999).
[CrossRef] [PubMed]

Struct. Multidisc. Optim.

X. Huang, Y. M. Xie, B. Jia, Q. Li, S. W. Zhou, “Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity,” Struct. Multidisc. Optim. 46(3), 385–398 (2012).
[CrossRef]

Other

M. P. Bendsøe and O. Sigmund, Topology Optimisation: Theory, Methods, and Applications (Springer, 2003).

M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, 1996).

http://www.lumerical.com .

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Figures (6)

Fig. 1
Fig. 1

Schematic of the thin-film solar cell: (a) front view; (b) cross sectional view; (c) 3D view.

Fig. 2
Fig. 2

Schematic of a hierarchical silver particle in a thin-film solar cell: (a) the representative volume element; (b) two-level nanoshperes.

Fig. 3
Fig. 3

The vertical/horizontal cross sections of the electric intensity: (a) and (d) around the separately-optimized nanospheres for convex solar cell; (b) and (e) around the optimized nanospheres for convex solar cell; (c) and (f) around the optimized nanospheres for flat solar cell.

Fig. 4
Fig. 4

(a) The convergence history of the optimization process: (a) the short circuit current density; (b) five design parameters.

Fig. 5
Fig. 5

The relative absorption distribution per unit volume: (a) flat solar cell without nanostructure; (b) convex solar cell with rear-located optimized nanostructure; (c) flat solar cell with rear-located optimized nanostructure.

Fig. 6
Fig. 6

The short circuit current density in the sunlight spectrum for three solar cells.

Tables (3)

Tables Icon

Table 1 Specifications of two-scale nanostructure

Tables Icon

Table 2 The parameters and the performance of the convex solar cells

Tables Icon

Table 3 The parameters and the performance of the flat solar cells

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

θ k =arccos( 1+ 2( k1 ) / ( N1 ) )1kN.
φ k = φ k1 + 3.6 / N( 1 ( 1+ 2( k1 ) / ( N1 ) ) 2 ) .
J sc =e λ/( hc )QE( λ ) I AM1.5 ( λ ) dλ.

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